Age (years) of trees: 62, 71, 74, 75, 78, 89, 91, 93
a) Original Sample Mean: Find the mean of all 8 values from the sample above:
Activity: This one sample does not define the entire forest. What if we were to gather another sample of 8 trees? What might the mean from this sample be? We can attempt to answer this question using the trees we already have! Your task is to use the 8 trees as representative of the entire forest (units are years). This is reasonable, since the sample was randomly gathered in the first place.
Write each tree age on a "card". Place the cards on your desk (face down) and shuffle them well. Draw out one slip, and record the value in the table below. Put the paper back on the desk, and re-shuffle carefully again. Draw another one, and record the value in the table. Continue to repeat this process, drawing one at a time, replacing it each time, and continually shuffling.
b) Write down your 8 resampled "trees" below:
Re-sample #1
Find the mean of your new sample:
c) Do it one more time.
Re-sample #2
Find the mean of your new sample:
Even though we have not measured the age of every tree in this forest, every time we observe a sample of 8 trees, we have an estimate for the mean age of all trees. We can look at the different estimates to write down a range of values that likely captures the mean age of all trees in the forest.
d) At this point, you have three estimates for the mean (parts a, b, and c above). Write down the three estimates for the mean in order from smallest to largest.
Sample means, sorted from least to greatest:
e) There is a good chance that the mean age of all trees is somewhere close to the values you listed above. Try to finish this sentence by filling in the blanks.
“I am pretty confident that the mean age of all trees in this forest is between and years.”